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Erik Strand
pit
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07d39a0c
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07d39a0c
authored
Apr 04, 2019
by
Erik Strand
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---
title
:
Problem Set
7
---
## (9.1)
{:.question}
Optics (as well as most of physics) can be derived from a global law as well as a local one, in this
case Fermat’s Principle: a light ray chooses the path between two points that minimizes the time to
travel between them. Apply this to two points on either side of a dielectric interface to derive
Snell’s Law.
## (9.2)
### (a)
{:.question}
Use Fresnel’s equations and the Poynting vectors to find the reflectivity and transmissivity of a
dielectric interface, defined by the ratios of incoming and outgoing energy.
### (b)
{:.question}
For a glass–air interface (n = 1.5) what is the reflectivity at normal incidence?
### (c)
{:.question}
What is the Brewster angle?
### (d)
{:.question}
What is the critical angle?
## (9.3)
{:.question}
Consider a wave at normal incidence to a dielectric layer with index $$n_2$$ and thickness $$d$$
between layers with indices $$n_1$$ and $$n_3$$.
### (a)
{:.question}
What is the reflectivity? Think about matching the boundary conditions, or about the multiple
reflections.
### (b)
{:.question}
Can you find values for $$n_2$$ and $$d$$ such that the reflection vanishes?
## (9.4)
{:.question}
Consider a ray starting with a height $$r_0$$ and some slope, a distance $$d_1$$ away from a thin
lens with focal length $$f$$. Use ray matrices to find the image plane where all rays starting at
this point rejoin, and discuss the magnification of the height $$r_0$$.
## (9.5)
{:.question}
Common CD players use an AlGaAs laser with a 790 nm wavelength.
### (a)
{:.question}
The pits that are read on a CD have a diameter of roughly $$1
\s
i{
\m
u m}$$ and the optics are
diffraction-limited; what is the beam divergence angle?
### (b)
{:.question}
Assuming the same geometry, what wavelength laser would be needed to read $$0.1
\s
i{
\m
u m}$$ pits?
### (c)
{:.question}
How large must a telescope mirror be if it is to be able to read a car’s license plate in visible
light ($$
\l
ambda
\a
pprox 600
\s
i{nm}$$) from a Low Earth Orbit (LEO) of 200 km?
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